<h2>Problem 30</h2>
<div style="color:#666;font-size:80%;">08 November 2002</div><br />
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<p>Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:</p>
<blockquote>1634 = 1<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 6<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 3<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 4<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /><br />
8208 = 8<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 2<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 0<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 8<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /><br />
9474 = 9<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 4<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 7<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> + 4<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /></blockquote>
<p class='info'>As 1 = 1<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /> is not a sum it is not included.</p>
<p>The sum of these numbers is 1634 + 8208 + 9474 = 19316.</p>
<p>Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.</p>

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